Non-equilibrium dynamics and phase transitions in Potts model and interacting Ehrenfest urn model

Abstract

We show that the recently proposed interacting Ehrenfest M-urn model at equilibrium (Cheng et al., 2020) can be exactly mapped to a mean-field M-state Potts model. By exploiting this correspondence, we show that the M-state Potts model with M≥3, with transition rates motivated by the non-equilibrium urn model, can exhibit rich non-equilibrium spin dynamics such as non-equilibrium steady states and non-equilibrium periodic states. Monte Carlo simulations of the 3-state Potts model are performed to demonstrate explicitly the first-order transitions for the equilibrium and non-equilibrium steady states, as well as the far-from-equilibrium periodic states.